svode mu Question 3: Tisgorg If the decision maker has the following utility function, u(w)--aw, where a >0 Derive the Jensen's inequality based on the utility given?
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- Suppose Jimi has reference dependent preferences over guitars and money as in Tversky and Kahneman (1991). His utility functions are given below. Gains Gains 400 -2 -2 2 Guitars Losses Losses |-600 -2 What is the least amount of money Jimi is willing to accept to sell one of his guitars? (just enter a dollar amount, i.e., "1000", not "$1000"1. For each of the following scaling functions for a von Neumann-Morgenstern utility func- tion, determine the Marginal Rate of Substitution between X1 and X2 and the equation for an indifference curve through the consumption bundle (100,100) (solve for X2 on the left hand side of the equation). State 1 is the bad outcome that occurs with probability 0.2 and State 2 the good outcome that occurs with probability 0.8. Graph these indif- ference curves and comment on what you see. Is a consumer with these preferences risk averse, risk neutral, or risk loving? (a) V(X) = InX (b) V(X)= VX (c) V(X)= X (d) V(X)= X²Suppose X = R k + for some k ≥ 2, and we define x = (x1 , …, xk ) ≥ = (y1 , …, yk ) if x ≥ y; that is, if for each i = 1, …, k, xi ≥ yi . (This is known as the Pareto ordering on R k + ; it plays an important role in the context of social choice theory in Chapter 8.) (a) Show that ≥ is transitive but not complete. (b) Characterize ≥ Is asymmetric? Is≥ Negatively transitive? Prove your assertions. (c) Characterize ~ defined from ≥ in the usual fashion; that is, x ~ y if x ≥ y and y x. Is ~ reflexive? Symmetric? Transitive? Prove your assertions.
- The price of X is $20 and the price of Y is $40. Y 30 Uz 24 40 Units of good X based on the graph, at point B, Multiple Choiİce < Prev B. 14 Units of good Yfor which utility function recardian equivalence does not hold?The following relation > on N = {W, X, Y, Z} with W > W,Z X > W, X, Y, Y > W, X, Y, Z Z Z W, X, Y, Z, is a preference relation. (You do not have to verify this.) (a) Is a preference ordering on N? Justify your answer. (b) Jake uses to determine his choice from N. Write down Jake's choice from N. (c) When making his choice from N, Adam uses a cardinal utility function U with U(W) 5, U(X) = x, U(Y) = 3x and U(Z) = 1, where x € Y. Given that Adam is indifferent between X, Y, Z and WX, Y, find the value of x. =
- The Foundations of Behavioral Economic Analysis Consider the following property of choice correspondence : Show that maximization of complete and transitive preference satisfies β-axiom. I need this ASAPT/F Explain If preference is strongly convex, the utility function will exhibit dimin- ishing marginal utility (MU).If Utility =.5lnX++3Z+10+4√W then Marginal utility from W is...
- Give an example of monotonic preferenceIs the pareto principle generally accepted as true or accurate? Or is it considered not true?Given Katy's utility function, she needs to give up increasing amounts of sleeping hours in order to visit one more party and remain as well off. O True False Unable to be determined